Re: Battletech, but with like... dragons and stuff.
Change your hatchets out for claws, according to current Total Warfare rules you cannot make more than one physical attack per turn excepting punching or claws. Besides I think that probably fits your aesthetic a bit better.
Claws rules (Technically not tech 1 but they're freaking claws!)
According to Pg 288 Tactical Operations: Claws weigh 1 ton and occupy 1 critical slot per 15 tons of mech weight and automatically replaces the hand.
They do damage based on tonnage divide by 7 and add a +1 to hit, but they still hit on the punch table
Edit: Oh and Wayne there are actually Dragon mounted Infantry in Technical Readout 3085 so they are out there I think they are Marik troops